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Encyclopedia > Units of measurement
The former Weights and Measures office in Middlesex, England.

In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures developed long ago for commercial purposes. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Metrology (from Greek metron (measure), and -logy) is the science of measurement. ... Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measurement. ... A physical quantity is either a quantity within physics that can be measured (e. ... This article is in need of attention from an expert on the subject. ... Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ...

Science, medicine, and engineering often use larger and smaller units of measurement than those used in day to day life and talk about them more exactly. The judicious selection of the units of measure can aid researchers in problem solving (see, for example dimensional analysis). A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For the chemical substances known as medicines, see medication. ... Engineering is the discipline of acquiring and applying knowledge of design, analysis, and/or construction of works for practical purposes. ... Problem solving forms part of thinking. ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...

A unit of measurement is a standardised quantity of a physical property, used as a factor to express occurring quantities of that property. Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Some human-referenced units of measurement Units of measurement were among the earliest tools invented by humans. ... Quantity is a kind of property which exists as magnitude or multitude. ... A baby wearing many items of winter clothing: headband, cap, fur-lined coat, shawl and sweater. ... Barter is a simple form of trade where goods or services are exchanged for a certain amount of other goods or services, i. ...

The earliest known uniform systems of weights and measures seem to have all been created sometime in the 4th and 3rd millennia BC among the ancient peoples of Mesopotamia, Egypt and the Indus Valley, and perhaps also Elam in Persia as well. The 4th millennium BC saw major changes in human culture. ... The 3rd millennium BC spans the Early to Middle Bronze Age. ... Mesopotamia was a cradle of civilization geographically located between the Tigris and Euphrates rivers, largely corresponding to modern-day Iraq. ... Excavated ruins of Mohenjo-daro. ... Elam (Persian: ØªÙ…Ø¯Ù† Ø§ÛŒÙ„Ø§Ù…) is one of the oldest recorded civilizations. ... Anthem SorÅ«d-e MellÄ«-e ÄªrÄn Â² Capital (and largest city) Tehran Official languages Persian Demonym Iranian Government Islamic Republic  -  Supreme Leader  -  President Unification  -  Unified by Cyrus the Great 559 BCE   -  Parthian (Arsacid) dynastic empire (first reunification) 248 BCE-224 CE   -  Sassanid dynastic empire 224â€“651 CE   -  Safavid dynasty...

Many systems were based on the use of parts of the body and the natural surroundings as measuring instruments. Our present knowledge of early weights and measures comes from many sources.

## Systems of measurement

This derivation of the Vitruvian Man by Leonardo da Vinci, depicts nine historical units of measurement: the Yard, the Span, the Cubit, the Flemish Ell, the English Ell, the French Ell, the Fathom, the Hand , and the Foot. The Vitruvian man was drawn to scale, so the units depicted are displayed with their proper historical ratios.

### Metric systems

A number of metric systems of units have evolved since the adoption of the original metric system in France in 1791. The current international standard metric system is the International system of units. An important feature of modern systems is standardization. Each unit has a universally recognized size. The International System of Units (symbol: SI) (for the French phrase Syst me International dUnit s) is the most widely used system of units. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... â€œStandardâ€ redirects here. ...

### Natural systems

While the above systems of units are based on arbitrary unit values, formalised as standards, some unit values occur naturally in science. Systems of units based on these are called natural units. Similar to natural units, atomic units (au) are a convenient system of units of measurement used in atomic physics. In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ... Atomic units (au) form a system of units convenient for electromagnetism, atomic physics, and quantum electrodynamics, especially when the focus is on the properties of electrons. ... In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. ... Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ...

Also a great number of strange and non-standard units may be encountered. These may include: the solar mass, the ton of TNT, the Hiroshima atom bomb and the weight of an elephant. Strange and whimsical units are sometimes used by scientists, especially physicists and mathematicians, and other technically-minded people such as engineers and programmers, as bits of dry humor combined with putative practical convenience. ... R-phrases S-phrases Related Compounds Related compounds picric acid hexanitrobenzene Except where noted otherwise, data are given for materials in their standard state (at 25 Â°C, 100 kPa) Infobox disclaimer and references Trinitrotoluene (TNT) is a chemical compound with the formula C6H2(NO2)3CH3. ... For other uses, see Hiroshima (disambiguation). ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ... Genera and Species Loxodonta Loxodonta cyclotis Loxodonta africana Elephas Elephas maximus Elephas antiquus â€  Elephas beyeri â€  Elephas celebensis â€  Elephas cypriotes â€  Elephas ekorensis â€  Elephas falconeri â€  Elephas iolensis â€  Elephas planifrons â€  Elephas platycephalus â€  Elephas recki â€  Stegodon â€  Mammuthus â€  Elephantidae (the elephants) is a family of pachyderm, and the only remaining family in the order Proboscidea...

## Base and derived units

Different systems of units are based on different choices of a set of fundamental units. The most widely used system of units is the International System of Units, or SI. There are seven SI base units. All other SI units can be derived from these base units. A set of fundamental units is a set of units for physical quantities from which every other unit can be generated. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The SI system of units defines seven SI base units: physical units defined by an operational definition. ... SI derived units are part of the SI system of measurement units and are derived from the seven SI base units. ...

For most quantities a unit is absolutely necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given.

But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the base units. Other units are derived units. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Which units are considered base units is a matter of choice.

The base units of SI are actually not the smallest set. Smaller sets have been defined. There are sets in which the electric and magnetic field have the same unit. This is based on physical laws that show that electric and magnetic field are actually different manifestations of the same phenomenon. The SI system of units defines seven SI base units: physical units defined by an operational definition. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... For the indie-pop band, see The Magnetic Fields. ...

## Calculations with units

### Units as dimensions

Any value of a physical quantity is expressed as a comparison to a unit of that quantity. For example, the value of a physical quantity Z is written as the product of a unit [Z] and a numerical factor: A physical quantity is either a quantity within physics that can be measured (e. ...

$Z = n times [Z] = n [Z].$

The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. In formulas the unit [Z] can be treated as if it were a kind of physical dimension: see dimensional analysis for more on this treatment. 2-dimensional renderings (ie. ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...

A distinction should be made between units and standards. A unit is fixed by its definition, and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit, and realizes that unit only under certain physical conditions. For example, the metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be one metre long only at a certain temperature.

### Guidelines

• Treat units like variables. Only add like terms. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metres per second (m/s). See dimensional analysis. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m²/s²).
• Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to one kg·m/s². This creates the possibility for units with multiple designations, for example: the unit for surface tension can be referred to as either N/m (newtons per metre) or kg/s² (kilograms per second squared).

Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ... This box:      Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. ...

### Expressing a physical value in terms of another unit

Conversion of units involves comparison of different standard physical values, either of a single physical quantity or of a physical quantity and a combination of other physical quantities. Conversion of units refers to conversion factors between different units of measurement for the same quantity. ...

Starting with:

$Z = n_i times [Z]_i$

just replace the original unit [Z]i with its meaning in terms of the desired unit [Z]j, e.g. if $[Z]_i = c_{ij} times [Z]_j$, then:

$Z = n_i times (c_{ij} times [Z]_j) = (n_i times c_{ij}) times [Z]_j$

Now ni and cij are both numerical values, so just calculate their product.

Or, which is just mathematically the same thing, multiply Z by unity, the product is still Z:

$Z = n_i times [Z]_i times ( c_{ij} times [Z]_j/[Z]_i )$

For example, you have an expression for a physical value Z involving the unit feet per second ([Z]i) and you want it in terms of the unit miles per hour ([Z]j):

1. Find facts relating the original unit to the desired unit:
1 mile = 5280 feet and 1 hour = 3600 seconds
2. Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:
$1 = frac{1,mathrm{mi}}{5280,mathrm{ft}}quad mathrm{and}quad 1 = frac{3600,mathrm{s}}{1,mathrm{h}}$
3. Last,multiply the original expression of the physical value by the fraction, called a conversion factor, to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are dimensionless and have a numerical value of one, multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.
$52.8,frac{mathrm{ft}}{mathrm{s}} = 52.8,frac{mathrm{ft}}{mathrm{s}} frac{1,mathrm{mi}}{5280,mathrm{ft}} frac{3600,mathrm{s}}{1,mathrm{h}} = frac {52.8 times 3600}{5280},mathrm{mi/h} = 36,mathrm{mi/h}$

Or as an example using the metric system, you have a value of fuel economy in the unit litres per 100 kilometres and you want it in terms of the unit microlitres per metre: This article lists conversion factors between a number of units of measurement. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... One redirects here. ...

$mathrm{frac{9,rm{L}}{100,rm{km}}} = mathrm{frac{9,rm{L}}{100,rm{km}}} mathrm{frac{1000000,rm{mu L}}{1,rm{L}}} mathrm{frac{1,rm{km}}{1000,rm{m}}} = frac {9 times 1000000}{100 times 1000},mathrm{mu L/m} = 90,mathrm{mu L/m}$

## Real-world implications

One example of the importance of agreed units is the failure of the NASA Mars Climate Orbiter, which was accidentally destroyed on a mission to the planet Mars in September 1999 instead of entering orbit, due to miscommunications about the value of forces: different computer programs used different units of measurement (newton versus pound force). Enormous amounts of effort, time, and money were wasted.[2][3] For other uses, see NASA (disambiguation). ... Artists conception of the Mars Climate Orbiter Mars Climate Orbiter during tests The Mars Climate Orbiter (formerly the Mars Surveyor 98 Orbiter) was one of two spacecraft in the Mars Surveyor 98 program, the other being the Mars Polar Lander (formerly the Mars Surveyor 98 Lander). ... This article is about the astronomical term. ... Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... For other uses, see Newton (disambiguation). ... A pound or pound-force (abbreviations: lb, lbf, or lbf) is a unit of force. ...

On April 15, 1999 Korean Air cargo flight 6316 from Shanghai to Seoul was lost due to the crew confusing tower instructions (in metres) and altimeter readings (in feet). Three crew and five people on the ground were killed. Thirty seven were injured.[2][4] is the 105th day of the year (106th in leap years) in the Gregorian calendar. ... Events of 2008: (EMILY) Me Lesley and MIley are going to China! This article is about the year. ... Korean Air (formerly Korean Air Lines) (KRXS: 003490) (Korean Air Daehan Hanggong) is the flag carrier airline of Korea, its global headquarters are located in Seoul, Korea. ... For other uses, see Shanghai (disambiguation). ... Short name Statistics Location map Map of location of Seoul. ...

## References

1. ^ US Metric Act of 1866
2. ^ a b Unit Mixups (from US Metric Association)
3. ^ ftp://ftp.hq.nasa.gov/pub/pao/reports/1999/MCO_report.pdf NASA (1999-11-10) Mars Climate Orbiter Mishap Investigation Board Phase I Report
4. ^ Korean Air incident
• Appendix B of NIST Handbook 44, (2002) National Institute of Science and Technology

Results from FactBites:

 Units of Measurement (845 words) We measure the length of a race in meters, but the length of the long jump event in feet and inches. There are two systems for land measurement (one based on the yard and the other on the rod) and a third system for distances at sea. In this way, all the units of measurement Americans use every day are based on the standards of the metric system.
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